Answered

Get personalized and accurate responses to your questions with IDNLearn.com. Our Q&A platform is designed to provide quick and accurate answers to any questions you may have.

Determine if each set of ordered pairs represents a function.

A. [tex]\((2, 3), (6, -5), (-1, 3)\)[/tex]

B. [tex]\((1, 9), (-3, -2), (1, -4)\)[/tex]

C. [tex]\((7, -4), (0, 9), (2, -2)\)[/tex]

D. [tex]\((0, 3), (0, 7), (4, 0)\)[/tex]

E. [tex]\((-6, 5), (-5, 6), (8, 2)\)[/tex]

Options:
1. Function
2. Not a Function

Sagot :

GinnyAnsweridn
To determine whether each set of ordered pairs represents a function, we need to check if each input (or [tex]\( x \)[/tex]-value) is associated with exactly one output (or [tex]\( y \)[/tex]-value). In simple terms, no [tex]\( x \)[/tex]-value should be repeated with different [tex]\( y \)[/tex]-values.

Let's analyze each set of ordered pairs in detail:

1. [tex]\((2,3), (6,-5), (-1,3)\)[/tex]:

- [tex]\( x \)[/tex]-values: [tex]\( 2, 6, -1 \)[/tex]
- All [tex]\( x \)[/tex]-values are unique.

Therefore, this set represents a function.

2. [tex]\((1,9), (-3,-2), (1,-4)\)[/tex]:

- [tex]\( x \)[/tex]-values: [tex]\( 1, -3, 1 \)[/tex]
- The [tex]\( x \)[/tex]-value [tex]\( 1 \)[/tex] is repeated with different [tex]\( y \)[/tex]-values ([tex]\( 9 \)[/tex] and [tex]\( -4 \)[/tex]).

Therefore, this set does not represent a function.

3. [tex]\((7,-4), (0,9), (2,-2)\)[/tex]:

- [tex]\( x \)[/tex]-values: [tex]\( 7, 0, 2 \)[/tex]
- All [tex]\( x \)[/tex]-values are unique.

Therefore, this set represents a function.

4. [tex]\((0,3), (0,7), (4,0)\)[/tex]:

- [tex]\( x \)[/tex]-values: [tex]\( 0, 0, 4 \)[/tex]
- The [tex]\( x \)[/tex]-value [tex]\( 0 \)[/tex] is repeated with different [tex]\( y \)[/tex]-values ([tex]\( 3 \)[/tex] and [tex]\( 7 \)[/tex]).

Therefore, this set does not represent a function.

5. [tex]\((-6,5), (-5,6), (8,2)\)[/tex]:

- [tex]\( x \)[/tex]-values: [tex]\( -6, -5, 8 \)[/tex]
- All [tex]\( x \)[/tex]-values are unique.

Therefore, this set represents a function.

In summary:

1. [tex]\((2,3), (6,-5), (-1,3)\)[/tex] - Function
2. [tex]\((1,9), (-3,-2), (1,-4)\)[/tex] - Not a Function
3. [tex]\((7,-4), (0,9), (2,-2)\)[/tex] - Function
4. [tex]\((0,3), (0,7), (4,0)\)[/tex] - Not a Function
5. [tex]\((-6,5), (-5,6), (8,2)\)[/tex] - Function

So the final results are:
- [tex]\((2,3), (6,-5), (-1,3)\)[/tex] - Function
- [tex]\((1,9), (-3,-2), (1,-4)\)[/tex] - Not a Function
- [tex]\((7,-4), (0,9), (2,-2)\)[/tex] - Function
- [tex]\((0,3), (0,7), (4,0)\)[/tex] - Not a Function
- [tex]\((-6,5), (-5,6), (8,2)\)[/tex] - Function
We appreciate your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Thank you for visiting IDNLearn.com. We’re here to provide accurate and reliable answers, so visit us again soon.